Chapter 6.2, Problem 30HP

To determine

To identify: The real-world situation for system of equations having one solution.

Explanation of Solution

Let $y$ represents the number of kgs of onions bought and $x$ represents the number of kgs of tomatoes bought. Assume, one kg of onions costs $\$25$ and one kg of tomatoes costs $\$60$ .

If we bought a total of $6$ kgs and spent a total of $\$220$ .

The system of equations represents the above situation are,

  $x+y=6$ --------(1)

  $25x+60y=220$ ---------(2)

The solution of the above system of equations represent the number of kgs of onions bought and number of kgs of tomatoes bought by the buyer.

Using substitution method,

Substituting $y=6-x$ from the 1^st equation in the 2^nd equation.

We get

  $\begin{array}{l}25x+60y=220\\ \Rightarrow 25x+60\left(6-x\right)=220\\ \Rightarrow 25x+60\left(6\right)-60\left(x\right)=220\\ \Rightarrow 25x+360-60x=220\\ \Rightarrow 25x-60x=220-360\\ \Rightarrow -35x=-140\\ \Rightarrow x=4\end{array}$

Substituting the value $x=4$ in $y=6-x$ ,

We get

  $\begin{array}{l}y=6-x\\ \Rightarrow y=6-4\\ \Rightarrow y=2\end{array}$

Therefore, the buyer bought $4$ kgs of onions and $2$ kgs of tomatoes.